Related papers: Intuitionism: an inspiration?
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
Recently we presented a concise survey of the formulation of the induction and coinduction principles, and some concepts related to them, in five different fields mathematical fields, hence shedding some light on the precise relation…
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…
This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.
We introduce an intuitionistic modal logic strictly contained in the intuitionistic modal logic IK and being an appropriate candidate for the title of ``minimal normal intuitionistic modal logic''.
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
This text (in Spanish) hopes to offer the reader a starting point to deliver good talks on mathematical topics.
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…
We provide an introduction to the old-standing problem of isometric immersions. We combine a historical account of its multifaceted advances, which have fascinated geometers and analysts alike, with some of the applications in the…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge; Brouwer disagrees on both…
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
An expository hitchhikers guide to some theorems in mathematics.
Intuitionistic epistemic logic introduces an epistemic operator, which reflects the intended BHK semantics of intuitionism, to intuitionistic logic. The fundamental assumption concerning intuitionistic knowledge and belief is that it is the…
Quantum probability theory and complex analysis for children.
The aim of the paper is to provide a rather gentle introduction into Donaldson-Thomas theory using quivers with potential. The reader should be familiar with some basic knowledge in algebraic or complex geometry. The text contains many…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
This article of mathematical education reflects author's experience with job applications and teaching methods and procedures to employ in the American Higher Education. It is organized as a standard questionnaire.
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…